Copy and paste the text into Script Editor, and then save the script into either the top-level /Library/Address Book Plug-Ins folder, or the same folder in your user's Library (depending on if you want the script globally available or not).
After installation, when you click a Contact's Phone number (the label portion) in Address Book, you will have an option to 'Dial Using Landline.' When you select it, the script will dial the number through the internal modem (make sure you have a modem phone/cable plugged in). A pop-up a dialogue asking if you want to 'Disconnect' or 'Pick-Up Handset' will then be displayed. If you choose 'Disconnect,' the script will drop the connection straight away; if you choose 'Pick-Up Handset,' the script will drop the connection in two seconds (the approximate time it should take for you to pick up your handset.
The script uses the Internet Connection application to dial out. This should, for the most part, remain hidden, but the app will be visible in the dock.
I also created a second script using a different dialing technique -- via the efax command line app. Since Internet Connect isn't used, this should be even more transparent than the first script (install it in the same manner as above).
[robg adds: I haven't tested these scripts...]

